Analysis of the localization of deformation and the complete stress–strain relation for mesoscopic heterogeneous brittle rock under dynamic uniaxial tensile loading

Stress redistribution induced by excavation results in the tensile zone in parts of the surrounding rock mass. It is significant to analyze the localization of deformation and damage, and to study the complete stress–strain relation for mesoscopic heterogeneous rock under dynamic uniaxial tensile loading. On the basis of micromechanics, the complete stress–strain relation including linear elasticity, nonlinear hardening, rapid stress drop and strain softening is obtained. The behaviors of rapid stress drop and strain softening are due to localization of deformation and damage. The constitutive model, which analyze localization of deformation and damage, is distinct from the conventional model. Theoretical predictions have shown to consistent with the experimental results.     

Constitutive relationship of brittle rock subjected to dynamic uniaxial tensile loads with microcrack interaction effects

A micromechanical model is proposed to describe both stable and unstable damage evolution in microcrack-weakened brittle rock material subjected to dynamic uniaxial tensile loads. The basic idea of the present model is to classify the constitution relationship of rock material subjected to dynamic uniaxial tensile loads into four stages including some of the stages of linear elasticity, pre-peak nonlinear hardening, rapid stress drop, and strain softening, and to investigate their corresponding micromechanical damage mechanisms individually. Special attention is paid to the transition from structure rearrangements on microscale to the macroscopic inelastic strain, to the transition from distribution damage to localization of damage and the transition from homogeneous deformation to localization of deformation. The influence of all microcracks with different sizes and orientations are introduced into the constitutive relation by using the statistical average method. Effects of microcrack interaction on the complete stress-strain relation as well as the localization of damage for microcrack-weakened brittle rock material are analyzed by using effective medium method. Each microcrack is assumed to be embedded in an approximate effective medium that is weakened by uniformly distributed microcracks of the statistically-averaged length depending on the actual damage state. The elastic moduli of the approximate effective medium can be determined by using the dilute distribution method. Micromechanical kinetic equations for stable and unstable growth characterizing the ‘process domains’ of active microcracks are taken into account. These ‘process domains’ together with ‘open microcrack domains’ completely determine the integration domains of ensemble averaged constitutive equations relating macro-strain and macro-stress. Theoretical predictions have shown to consistent with the experimental results.     

ANALYSIS OF THE LOCALIZATION OF DAMAGE AND THE COMPLETE STRESS-STRAIN RELATION FOR MESOSCOPIC HETEROGENEOUS ROCK UNDER UNIAXIAL TENSILE LOADING

The mechanical behavior of rock under uniaxial tensile loading is different from that of rock under compressive loads. A micromechanics-based model was proposed for mesoscopic heterogeneous brittle rock undergoing irreversible changes of their microscopic structures due to microcrack growth. The complete stress-strain relation including linear elasticity, nonlinear hardening, rapid stress drop and strain softening was obtained. The influence of all microcracks with different sizes and orientations were introduced into the constitutive relation by using the probability density function describing the distribution of orientations and the probability density function describing the distribution of sizes. The influence of Weibull distribution describing the distribution of orientations and Rayleigh function describing the distribution of sizes on the constitutive relation were researched. Theoretical predictions have shown to be consistent with the experimental results.     

Localization of deformation and stress–strain relation for mesoscopic heterogeneous brittle rock materials under unloading

Stress redistribution induced by excavation of underground engineering and slope engineering results in the unloading zone in parts of surrounding rock masses. The mechanical behaviors of crack-weakened rock masses under unloading are different from those of crack-weakened rock masses under loading. A micromechanics-based model has been proposed for brittle rock material undergoing irreversible changes of their microscopic structures due to microcrack growth when axial stress is held constant while lateral confinement is reduced. The basic idea of the present model is to classify the constitution relation of rock material into four stages including some of the stages of linear elasticity, pre-peak nonlinear hardening, rapid stress drop, and strain softening, and to investigate their corresponding micromechanical damage mechanisms individually. Special attention is paid to the transition from structure rearrangements on microscale to the macroscopic inelastic strain, to the transition from distribution damage to localization of damage and the transition from homogeneous deformation to localization of deformation. The closed-form explicit expression for the complete stress–strain relation of rock materials containing cracks under unloading is obtained. The results show that the complete stress–strain relation and the strength of rock materials under unloading depend on the crack spacing, the fracture toughness of rock materials, orientation of the cracks, the crack half-length and the crack density parameter.     

Triaxial compressive behavior of rock with mesoscopic heterogenous behavior: Strain energy density factor approach

The strain energy density factor approach is used in conjunction with a micromechanics model to investigate the condition and direction of shear failure for brittle rock subjected to triaxial compression. Moderate confinement in addition to localized deformation and damage are considered. Quantified are the effects of the various geometric and load parameters that involve the interaction of microcrack, friction and the confining pressure such that the path of the wing crack is taken into account. The influence of all microcracks with different orientations are introduced into the constitutive relation. The closed-form solution for the complete stress–strain relation of rock containing microcracks is obtained. It is shown that the complete stress–strain relationship includes linear, nonlinear hardening, rapid stress drop and strain softening effects. The theoretical results show that deviation of the direction of wing cracks from the line of the pre-existing crack decreases with increasing confinement pressure and friction coefficient. Theoretical predictions and experimental results show good agreement.     

Upper and lower bounds for constitutive relation of crack-weakened rock masses under dynamic compressive loads

A micro-mechanics-based model is proposed to investigate the rate-dependent constitutive relation for crack-weakened rock masses subjected to dynamic compressive loads. The present micro-mechanical model reveals that the nucleation, growth and coalescence of sliding cracks dominate the failure and macroscopic properties of crack-weakened rock masses subjected to dynamic compressive loads. The interactions among multiple parallel sliding cracks in crack-weakened rock masses subjected to dynamic compressive loads are examined asymptotically in an explicit and quantitative manner in order to reveal fully their so-called shielding and magnification effects on the stress–strain relation. Based on the micro-mechanical framework and the asymptotic analysis, analytical upper and lower bounds are proposed for the rate-relation for rock masses containing multiple rows of echelon cracks subjected to dynamic compressive loads. The factors that affect the rate-dependent properties of crack-weakened rock masses have been analyzed. The strain energy density factor approach, which is related to crack growth velocity and dynamic fracture toughness of rock material, is employed in the analysis. The rate-dependent constitutive relation of crack-weakened rock masses is derived from micro-mechanical framework and the asymptotic analysis. The closed-form explicit expression for the rate-dependent constitutive relation of rock masses containing echelon cracks subjected to dynamic compressive loads is obtained. Finally, the present model is used to analyze the complete stress–strain relation and strength for jointed rock masses at shiplock slope of the Three Gorges Dam.     

冲击载荷下盐岩的力学性能和本构关系研究

利用直径75mm的大尺寸SHPB实验装置开展盐岩的动态压缩性能实验研究,得到了其动态应力应变曲线。分析表明,在冲击压缩载荷作用下,盐岩材料有明显的损伤软化现象和应变率效应。针对实验曲线,通过引入描述材料强度随应变率强化的应变率增强因子和随不可逆变形发展而弱化的损伤因子,提出了含损伤率的相关动态本构模型,拟合得到的本构方程形式比较简单,能够较好地反映盐岩动态实验加载过程的主要特征,具有一定的工程应用价值。     

Dynamic damage constitutive relation of mesoscopic heterogenous brittle rock under rotation of principal stress axes

A micro-mechanics-based model is developed to investigate microcrack damage mechanism of four stages of brittle rock under rotation of the principal stress axes. They consist of linear elastic, non-linear hardening, rapid stress drop and strain softening. The frictional sliding crack model is applied to analyze microcracks nucleation, propagation and coalescence. The strain energy density factor approach is applied to determine the critical condition of microcrack nucleation, propagation and coalescence. The inelastic strain increments are formulated within the framework of thermodynamics with internal variables. Rotation of principal stress axes affect the dynamic damage constitutive relationship and the failure strength of brittle rock.     

复杂加载下混凝土的弹塑性本构模型

混凝土材料在不同应力路径下或复杂加载条件下会表现出差异性显著的应力应变关系,在小幅循环加载条件下,其应力应变关系会表现出类似于弹性变形的滞回曲线.在不同应力水平下,混凝土的应力应变关系以及破坏特性都具有静水压力相关特点,即随着静水压力增大,各向异性强度特性弱化.此外,混凝土受压及受拉破坏机理不同,因而对应于混凝土硬化损伤亦有不同,即可分为受压硬化损伤,受拉硬化损伤及两者的混合硬化损伤类型.基于Hsieh模型,对该模型进行了三点改进.（1）针对小幅循环加载下混凝土无塑性变形的试验规律,而模型中在应力水平较低的循环加载条件下始终存在塑性变形的预测问题,采用在边界面模型框架下,设置了应力空间的弹性域,初始屈服面与后续临界状态屈服面几何相似的假定.（2）基于广义非线性强度准则将原模型采用变换应力方法将其推广为三维弹塑性本构模型,采用变换后模型可合理的考虑不同应力路径对于子午面以及偏平面上静水压力效应形成的影响,并避免了边界面应力点奇异问题.（3）分别对拉压两种加载损伤模式建议了相应的硬化参数表达式,可分别用于描述上述加载中产生的应变软化及强度退化行为.基于多种加载路径模拟表明:所建立的三维弹塑性本构模型可合理地用于描述混凝土的一般应力应变关系特性.      

岩石单轴压缩作用下变形局部化的梯度塑性解

采用梯度塑性理论研究单轴压缩作用下岩石变形局部化,得到了单轴压缩作用下岩石变形局部化带宽度的一维、二维解析解,为实验测定内部材料长度参数提供了理论依据.     

The Three-Stage Model Based on Strain Strength Distribution for the Tensile Failure Process of Rock and Concrete Materials

A three-stage model is introduced to describe the tensile failure process of rock and concrete materials.Failure of the material is defined to contain three stages in the model,which include elastic deformation stage,body damage stage and localization damage stage.The failure mode change from uniform body damage to localization damage is expressed.The heterogeneity of material is described with strain strength distribution.The fracture factor and intact factor,defined as the distribution function of strain strength,are used to express the fracture state in the failure process.And the distributive parameters can be determined through the experimental stress-strain curve.     

侧向受拉脆性岩石压缩本构及蠕变失效研究

轴向压缩作用下,脆性岩石侧向应力严重影响岩石力学特性。侧向压应力影响下的轴向压缩岩石力学行为已经得到广泛研究,然而侧向拉应力对轴向压缩岩石力学行为影响研究很少。本文基于脆性岩石翼型裂纹扩展模型中,初始裂纹面法向应力与剪切应力的正负方向为判断依据,研究了侧向拉应力对轴向压缩力学行为的影响。发现恒定的侧向拉应力作用下,轴向压缩应力渐进变化过程中,脆性岩石内部细观初始裂纹面的法向应力只能为压缩应力,不存在拉应力情况。分析了从侧向压应力到拉应力转化过程中,脆性岩石轴向压应力与细观裂纹扩展长度关系、轴向压应力与轴向应变关系、岩石峰值强度、裂纹启裂应力及初始弹性模量的变化规律。并分析了侧向拉应力对岩石蠕变裂纹长度、裂纹速率、轴向应变及应变率演化曲线,以及对蠕变失效时间及稳态蠕变应变率的影响。讨论了侧向拉压应力突变转化以及侧向拉应力分级增大对轴向压缩岩石蠕变演化行为影响。该研究为深部地下工程围岩稳定性评价提供了一定理论依据。     

考虑裂纹闭合效应的岩石损伤本构关系

岩石中的预存裂纹只有在一定的法向压应力即裂纹闭合应力的作用下才可能闭合，其闭合过程与其方位和外加应力场有关，并且，即使对于裂纹已经完全闭合的岩石，如果裂纹闭合应力不同，则岩石的应力应交关系也不相同。本文建立了考虑裂纹闭合效应的岩石细观损伤力学模型，分析了裂纹闭合应力对岩石损伤演化过程和应力应变关系的影响。数值结果表明裂纹闭合应力显著地改变岩石的应力应变关系，表现为随裂纹闭合应力的增加，岩石的轴向应变变化较小，侧向应变和体积应变则大为增加。     

不同应变率下煤岩破坏特征及其本构模型

利用直径50 mm的分离式霍普金森压杆,对煤岩展开20～100 s?1动态应变率下的单轴冲击压缩试验,结合高速摄影分析其变形破坏特征,并建立基于Weibull统计分布和Drucker-Prager破坏准则的煤岩动态强度型统计损伤本构模型。试验结果表明:（1）煤岩动态应力-应变曲线存在明显的非线性特征,随应变率升高,动态抗压强度与弹性模量均呈线性增长且增幅显著,破坏形态由低应变率下的轴向劈裂破坏向高应变率下的压碎破坏过渡;（2）在动态应变率20～100 s?1下,煤岩破坏后碎块具有明显的分形特性,破碎块度分维值为1.9～2.2,且随着应变率的升高,煤岩破碎程度增大,碎块块度减小;（3）基于Weibull分布参数F₀、m和应变率的关系,修正煤岩的本构模型,并与试验结果进行对比,验证该模型的合理性。     

The mullins effect in uniaxial extension and its influence on the transverse vibration of a rubber string

This paper presents a study of the stress softening effect encountered in uniaxial extension and explores its effect on the small amplitude transverse vibration of a stretched rubber cord. An idealization of the uniaxial stressstrain behavior of a stress softening material is presented, the importance of the deformation history is emphasized, and parameters are introduced to track the deformation history. An extended investigation of a model proposed by Mullins and Tobin to quantify stress softening by introduction of a strain amplification factor is then presented. A major result derived from this model is shown to be consistent with results reported by others. The uniaxial stress softening theory is used to describe the transverse vibration behavior of a rubber string subjected to repeated stretching. This appears to be the first application of the softening model of Mullins and Tobin to a dynamical problem. Analytical results are compared with uniaxial stress-strain and transverse vibration experiments performed with buna-n, neoprene, and silicone rubber cords. Both types of experiments provide a simple and novel method to evaluate the predictive success of our uniaxial theory without the need for a specific constitutive model. The pseudoelastic response found in biological tissues is discussed in light of results obtained in the transverse vibration experiments.     

MICROMECHANICAL MODELLING OF STRAIN SOFTENING IN MICROCRACK-WEAKENED QUASI-BRITTLE MATERIALS

By using the concept of domain of microcrack growth(DMG),themicromechanisms of damage in quasi-brittle materials subjected to triaxial either tensileor compressive loading are investigated and the complete strew-strain relation includingfour stages is obtained from micromechanical analysis.The regime of pre-peaknonlinear hardening corresponds to the distributed damage,i.e.the stable propagationof microcracks.After the attainment of the ultimate strength of load-bearing capacity,some microcracks experience the second unstable growth and the distributed damage istransmitted to the localization of damage.These analyses improve our understanding ofthe hardening and softening behaviors of quasi-brittle materials.     

深部节理岩体塑性损伤耦合微面模型

采用微面模型理论和损伤力学方法,建立了节理岩体的弹塑性损伤耦合微面模型. 在节理岩体的微面上,将岩体视为由节理面与岩石组成的二元介质,以节理连通率作为岩体沿该方向的面积损伤变量,考虑微面法向拉应力和压应力下的不同塑性变形和损伤耦合作用机制,基于塑性理论建立了节理岩体的微面塑性损伤增量本构关系. 采用微面物理量与宏观物理量的几何约束模型,根据微面方向积分导出了节理岩体的宏观弹塑性增量本构关系. 编制了节理岩体微面模型的MARC有限元子程序,对节理岩体的单轴拉伸、压缩试验和泥浆压力作用下的井壁稳定问题进行了数值模拟研究. 数值计算结果表明,该模型能很好地揭示载荷作用下节理岩体的各向异性非弹性变形和次生节理演化过程.      

动力损伤后的脆性岩石静力蠕变断裂模型研究

应力波动力扰动下脆性岩石的静力蠕变特性,对深部地下工程围岩变形的评价有重要的实践意义.动力载荷作用导致的局部细观裂纹损伤严重影响脆性岩石蠕变力学行为.基于细观裂纹扩展与应力关系模型、动力扰动损伤演化函数、静动力载荷演化路径函数与黏弹性本构模型,提出一种应力波动力扰动下脆性岩石蠕变断裂特性的宏细观力学模型.其中动力损伤通过控制岩石内部细观裂纹数量变化实现.模型描述了应力波动力扰动下岩石的应变时间演化曲线,解释了岩石动力扰动下蠕变失效特性.研究了不同应力波幅值及周期影响下的脆性岩石应变-时间关系曲线,并通过试验结果验证了模型的合理性.讨论了动力损伤变化形式,突变发生时刻,突变量的大小对岩石蠕变失效特性的影响.分析了应力波幅值、周期对岩石动态动力损伤效应以及蠕变失效特性的影响.主要研究结果:动力损伤的变化值越大,岩石蠕变失效发生时间越短.冲击载荷扰动期间,动力损伤发生的时刻及增加的形式,对动力扰动后的岩石应变及蠕变破坏时间影响很小.动力损伤变化量随应力波幅值增加、周期减小而加速增大.应力波幅值越大、周期越小,岩石发生蠕变失效时间越短.     

岩体—界面系统剪切不稳定性分析

基于界面的刚塑性应变软化假设，分析了岩体－界面系统在端部剪力和岩体中分布剪切载荷共同作用下的变形、应力和损伤演化。利用位能原理和稳定性的能量准则，得到了岩体界面系统的不稳定性条件。分析结果表明，损伤区达到边界之前，系统可能是稳定的或者是不稳定的。依赖于分布剪切载荷和界面摩擦力的比较，若均布剪切载荷大于界面摩擦力，则系统不稳定，否则系统稳定；当损伤区达到边界之后，系统的不稳定性决定于载荷及界面材料性质，界面软化刚度系数和界面强度对于不稳定性有明显影响。